Numerical techniques in action in Maple V Release 5.

> with(DEtools):

To evaluate complicated functions (for plotting, for instance), some

sort of numerical approximation technique is often used:

> plot(sin(cos(x)*ln(x)),x=1..10);

Solving equations is another major area where numerical techniques

are often necessary:

> fsolve(sin(cos(x)*ln(x)),x,x=7..8);

If a function does not have an elementary antiderivative, the

Fundamental Theorem of Calculus is not much help in evaluating

a definite integral :

> int(sin(cos(x)*ln(x)),x=1..2);

But numerical techniques can be used to yield an approximate value:

> evalf(int(sin(cos(x)*ln(x)),x=1..10));

Solving differential equations is another area where numerical techniques

are often necessary:

> DEplot(diff(y(x),x) = y(x)*sin(cos(x)),y(x),x=1..5,y=-10..10,{[y(1)=4]},linecolor=black);

Numerical Analysis (MATH 371) will cover these topics and others, developing algorithms

like those used by Maple, analyzing their behavior and efficiency, and applying them

to solve problems from many areas of mathematics and its applications.